<"A linear function on a coordinate plane passes through (minus 4, minus 3), (minus 1, 0), (0, 1), and (3, 4)"/>

The given points are (-4, -3), (-1, 0), (0, 1), and (3, 4).

Step 1: Check if the points lie on the same line To do this, we can calculate the slope between each pair of points and see if it's the same. The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).

Let's calculate the slope between the first two points (-4, -3) and (-1, 0): Slope = (0 - (-3)) / (-1 - (-4)) = 3 / 3 = 1

Now, let's calculate the slope between the second and third points (-1, 0) and (0, 1): Slope = (1 - 0) / (0 - (-1)) = 1 / 1 = 1

Finally, let's calculate the slope between the third and fourth points (0, 1) and (3, 4): Slope = (4 - 1) / (3 - 0) = 3 / 3 = 1

Since the slope is the same between all pairs of points, the points lie on the same line.

Step 2: Find the equation of the line A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept. We already know that the slope m is 1.

To find the y-intercept b, we can use one of the points and the slope in the equation. Let's use the point (0, 1): 1 = 1*0 + b So, b = 1

Therefore, the equation of the line is y = x + 1.